In iconic nature scenes, one shape is ubiquitous: the tree. Based on evolutionary biology’s findings about innate human preferences for savanna-like environments, Judith Heerwagen and other psychologists have focused on tree images as signals of refuge that offer the potential for shelter, shade, and nourishment. Trees and other vegetation have inspired the art and architecture of every culture throughout history, which suggests their universal appeal. One species in particular, the Acacia tortilis, dominates the African savannah, where its silhouette emblazoned on the human retina for thousands of millennia, and research verifies that people are drawn to its shape—broad, spreading canopies and branches close to the ground. In a study by Richard Coss and his colleagues, a diverse group of preschool children, regardless of nationality, background, or experience, consistently chose acacia-like trees as the most inviting, offering the greatest feelings of security. In a 2000 experiment conducted by Heerwagen and others for furniture manufacturer Herman Miller, people sitting at desks decorated with acacia images scored better in memory and problem-solving tests. So the acacia isn’t just visually pleasing—it actually elicits a physiological response. What’s so magical about this tree?

The theory is that a preference for fractal images is genetically imprinted.

The appeal of the acacia in truth may have nothing to do with its being recognized as a tree. Experiments by psychologist James Wise and others used skin conductance techniques to measure anxiety during aptitude tests and found that participants exposed to highly abstract acacia-like images were less stressed than those who saw photographs of thick forest scenes. In other words, simplified diagrams of one kind of tree shape were more successful than realistic representations of another. Three significant revelations result from these findings: first, people respond not just to actual vegetation but also to related imagery; second, the imagery need not be realistic or recognizable as vegetation; third, not all vegetation or plantlike imagery works equally well. The implications for design are enormous. Plenty of research shows that access to natural scenes promotes well-being, but these other studies also suggest that nonrepresentational patterns can have a similar impact. In other words, abstract design can be good for you.

In fact, as the experiment above suggests, the right kind of artificial imagery can be better than the wrong kind of natural imagery. The common goal of offering building occupants views of nature could be overly broad, since certain scenes—dense forests or barren plains, for example—are not as effective as others. More and more evidence suggests that the operative feature of acacia-like imagery is not its overt expression of the savanna but, instead, its underlying order—the structure known as a fractal. Coined by French mathematician Benoit Mandelbrot in 1975, the term (meaning "broken" or "fractured") refers to irregular geometry that is continuously self-similar at every scale. The natural world is replete with fractals—in spinning galaxies and spitting sunbursts, in splitting crystals and splintering lungs, in creeping coastlines and veining leaves, in forking rivers and shivering snowflakes, and—importantly for human perception—in the explosive joy of a tree. Touching everything everywhere, fractals have been dubbed the "fingerprints of nature" and the "thumbprint of God."

Natural fractals are not those computer-generated paisleys, such as Mandelbrot’s own, popularized in the late 1980s by James Gleick’s book Chaos. Statistically generated to be precisely self-identical at different scales, these patterns appear mechanically repetitive, stiff, and artificial. Naturally occurring fractals, however, are self-similar, not self-identical, so they look looser, softer, less rigid and mechanical, and this fact could be exactly what makes them seem natural to the eye (and more structurally resilient in trees).

Mathematicians categorize fractals by their density (D) on a scale of 1 to 2, 1 being a flat line and 2 being complete fill; environmentally, the open ocean approximates D=1, while a thick jungle approaches D=2. Experiments by physicist Richard Taylor and others repeatedly reveal that a large majority of people (94 percent in Taylor’s experiments) prefer a density around 1.3 or 1.4, which matches acacia- and savanna-like images, including the abstract diagrams from the Wise experiment. The theory is that a preference for these kinds of fractal images is genetically imprinted at a density we associate with the optimal environment for survival—too sparse means not enough sustenance, and too dense means not enough opportunity for surveillance. Using eye-tracking techniques, Taylor also has shown that we tend to scan our surroundings with a fractal pattern approximating the preferred density, even when that pattern doesn’t exist in the visual field. We seek out the desired imagery everywhere we look.

And not just in nature. Physicist J. C. Sprott has found that test subjects are invariably drawn to logarithmically produced figures called "strange attractors"—artificial images that look nothing like nature—if they conform to the same geometric characteristics of trees, clouds, and other natural fractals. And more and more studies are proving that some of the most lasting art, design, and architecture of various historic cultures the world over are fractal at the optimal density—oriental rugs, Islamic tiling, the "interior skies" of Persian domes, the Gothic tracery of Venetian palaces, housing patterns in the European villages, the Zen garden of Ryoanji in Kyoto. The profile of a Doric temple entablature is nearly identical to the mathematical sequence known as "the Devil’s Staircase." Life magazine named abstract expressionist Jackson Pollock "the greatest living painter in the United States" in 1949, when he was creating canvases now known to conform to the optimal fractal density. Taylor sees Pollock’s late paintings as the culmination of a lifelong effort to excavate the images buried in all our brains.

Stylistically, the differences among the stately lines of a Greek temple, the spare serenity of a Zen garden, and the riotous drips and drabs of a Jackson Pollock couldn’t be more pronounced, yet all of them display the organizing principles of natural systems, the geometry of life. In each of these cases, what evolved unconsciously over a lifetime or many generations of continual experimentation and refinement was a sensibility that can only be considered more natural. Fractals have been called a "universal aesthetic."

A disastrous failure of modernism was its blind faith in simplicity.

Again, such imagery isn’t just appealing to the eye—it actually relaxes us. Taylor has shown that fractals at the optimal density can reduce stress levels by as much as 60 percent. Abstract visual patterns can cause a physiological reaction—we actually feel them in our bodies. Imagine the possibilities. If we can apply such imagery at any scale of design—graphics, clothing, carpet, walls, buildings, cities—we can design things that not only are more likely to be enjoyed—they can help us feel better. The economic potential alone is momentous, since, as Taylor points out, the United States spends $300 billion a year dealing with stress-related illness. Just looking at something could help us all become healthier and wealthier.

Today many designers in various disciplines are experimenting with irregular patterning. Interface’s popular "Entropy" line of carpet tiles, inspired by the disheveled look of leaves on a forest floor, revolutionized the industry by developing a way for every tile to be different. The versatility makes replacement easy, and the irregularity makes everyday wear and tear less visible, extending the life of the carpet as a kind of eco-camouflage. The potentially overwhelming scale of large buildings, such as the U.S. Census Bureau headquarters, can be humanized using such irregular patterns on their surfaces. The fractal-like screen on the facade of the Airspace Tokyo housing structure provides both shade and a forestlike view from the interior. Experiments with such treelike patterns applied to hospital windows show measurable benefits among patients. In Fractal Cities, Michael Batty and Paul Longley demonstrate that laying out a street network as a fractal tree can optimize density and linear frontage, thereby lowering unit costs and the total area of land needed. The gradual "organic evolution" of medieval towns shows similar economy and elegance, which is why, say Batty and Longley, the form of such places is often described as more "natural."

Design can adopt nature’s rules, patterns, and forms—its laws of shape. Half a century ago, in the final chapter of The Death and Life of Great American Cities, Jane Jacobs became the first to apply the emerging science of organized complexity to design. "What makes an evening primrose open when it does?" she asked, quoting mathematician Warren Weaver, a pioneer in the field. Weaver asked the question in 1948, Jacobs in 1961, and design and science are just now beginning to learn the geometric principles of organized complexity. Jacobs urged designers to adopt "new strategies for thinking," but new strategies for shaping are equally urgent. We’ll need better knowledge and better tools to create things that are functionally and formally better suited to ecology. The geometry of complexity is the shape of ecology.

Yet, classical and modernist aesthetics both favor simpler, Euclidean shapes. "Geometrical figures are naturally more beautiful than irregular ones," according to Christopher Wren, architect of St. Paul’s Cathedral in London. "The square, the circle are the most beautiful," Wren said, and philosophers, artists, and designers from Plato to Le Corbusier have agreed. But science doesn’t. A growing body of literature attests to the instinctive appeal and resilient structure of subtler, more natural shapes. A disastrous failure of modernism was its blind faith in simplicity, and much of what people revile about many modernist buildings and cities is their blunt, inhumane, antiseptic forms.

"Why is geometry often called cold and dry?" asks Mandelbrot in The Fractal Geometry of Nature. "One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line." In the past, he recounts, mathematicians have tended to "flee from nature," disdaining its irregular, complex shapes as "pathological," a "gallery of monsters." Some fractals, marvels Mandelbrot, are "so oddly shaped that there are no good terms for them in either the sciences or the arts." By clinging to the overly simple, designers also have fled from nature. Euclid’s compass can’t capture God’s thumbprint. Creating a "morphology of the ‘amorphous,’" writes Mandelbrot, the geometry of complexity reveals "a totally new world of plastic beauty."

Imagine an aesthetic based purely on nourishing mind, body, and soul.

In their report for Herman Miller, Heerwagen and her team refer to images such as acacias and fractals as "Habitability Icons." Imagine an aesthetic founded on the iconography of habitability—a visual system based purely on nourishing mind, body, and soul. Natural aesthetics need not look overtly like nature, for instead of reproducing the pictorial image of vegetation, designers can learn from the principles and patterns of living forms. Can designers extrapolate the underlying order of life without losing its sensory appeal? Such an aesthetic could be at once groundbreaking and utterly grounded in nature.

Consider the strange attractor. In physics, an attractor is the condition toward which a system tends to evolve—a marble rolling in a round bowl, for example, eventually will come to rest at bottom center. The shape toward which a complex system evolves is a strange attractor. The movers and shakers of ecology, strange attractors shape much of nature—the dance of planets, the motion of oceans. Design can be such an attractor, a state of being toward which the world moves naturally—an accomplice to ecology. There are shapes and patterns that lure the human senses because they participate in larger forces unfolding over time, an eternal choreography not immediately detected but evident everywhere, all around us. With science and sensitivity, smart design can gracefully, beautifully tap into the abiding wonders and mysteries of the universe.